A golf-course operator must decide what greens fees (prices) to set on rounds of golf. Daily demand during the week is Pd = 36 –Qd/10 where Qd is the number of 18 hole rounds and Pd is the price per round. Daily demand on the weekend is Pw = 50 – Qw/12. As a practical matter, the capacity of the course is 240 rounds per day. Wear and tear on the golf course is negligible.

Question

A golf-course operator must decide what greens fees (prices) to set on rounds of golf.  Daily demand during the week is Pd = 36 –Qd/10 where Qd is the number of 18 hole rounds and Pd is the price per round.  Daily demand on the weekend is Pw = 50 – Qw/12.  As a practical matter, the capacity of the course is 240 rounds per day.  Wear and tear on the golf course is negligible. 
a)	Can the operator profit by charging different prices during the week and on the weekend? What greens fee should the operator set on weekdays and how many rounds will be played on the weekend?

b)	When weekend prices skyrocket, some weekend golfers choose to play during the week instead.  The greater the difference between weekday and weekend prices; the greater are the number of these defectors.  How might this factor affect the operator’s pricing policy
As weekend prices skyrocket more people will play golf during the week and eventually the weekend prices will drop and weekday prices.

Anonymous · Answer

The problem doesn't state what Pw is, so assuming that is the price per round on the weekend, then:
weekend profit = Pw x Qw
daily profit = Pd x Qd
Take the 1st derivative of each of these, set equal to zero, and solve for the maximum value of the profit.